Elliptic genus and vertex operator algebras (Q2471446)

The rigidity and vanishing theorem for the Dirac operator on the loop space twisted by general bundles of modules of vertex operator algebra is proved. Hence, it follows that an elliptic coholonomy should contain certain vertex operator algebra bundles. See also \textit{R. E. Borcherds}, Invent. Math. 109, No. 2, 405--444 (1992; Zbl 0799.17014); \textit{I. Frenkel, J. Lepowsky} and \textit{A. Meurman}, Vertex operator algebras and the monster. Pure and Applied Mathematics, 134. Boston etc.: Academic Press (1988; Zbl 0674.17001); \textit{C. Dong, H. Li} and \textit{G. Mason}, Commun. Math. Phys. 214, No. 1, 1--56 (2000; Zbl 1061.17025); \textit{K. Liu}, J. Differ. Geom. 41, No. 2, 343--396 (1995; Zbl 0836.57024).